Frequency estimation techniques for high dynamic trajectories

A comparison is presented of four different estimation techniques applied to the problem of continuously estimating the rapidly varying parameters of a sinusoidal signal, observed in the presence of additive noise. Frequency estimates are emphasized, although phase and/or frequency rate are also estimated by some of the algorithms. These parameters are related to the velocity, position, and acceleration of the maneuvering receiver or transmitter. Estimated performance at low carrier-to-noise ratios and high dynamics is investigated for the purpose of determining the useful operating range of an approximate maximum likelihood estimator, an extended Kalman filter, a cross-product automatic frequency loop and a phase-locked loop. Numerical simulations are used to evaluate performance while tracking a common trajectory exhibiting high dynamics     

Magnetospheric signatures of auroral disturbances during the passage of the solar wind’s CIR and sheath regions

Based on Polar satellite data, the authors have studied the auroral disturbances that arose during the passage by the Earth of compressed plasma regions formed in front of high-speed solar wind streams (the CIR region) and in front of magnetic clouds (the Sheath region). The aurorae observed by the Polar satellite possessed basic signatures of a substorm: a localized onset and expansion toward the pole and westward and eastward. However, in these cases they had a very large size in longitude and latitude and occupied a very large area. All disturbances observed by the Polar satellite during the Sheath and CIR regions of the solar wind in December of 1996, in 1997–1998, and in 2000 were analyzed. Eight events during disturbance development in the ionosphere, when the Geotail satellite was located in the plasma sheet of the magnetospheric tail, were selected. It is shown that in all selected cases some typical signatures of substorm development in the magnetospheric tail were observed, namely: (1) fast plasma flows (flow reversal, i.e., from tailwards to Earthwards) and (2) a sharp decrease of the total pressure, which followed an interval of total pressure increase. One can draw the conclusion that in the CIR and Sheath regions with a high solar wind density, substorm disturbances of a specific type are observed, with large latitudinal and longitudinal size (sometimes occupying the entire polar cap).     

Families of Periodic Solutions to the Beletsky Equation

A review of achievements in the investigation of the planar periodic oscillations and rotations of a satellite around its center of mass, which moves along an elliptic orbit in the central gravitational field, is presented. These oscillations and rotations of the satellite are described by an ordinary differential equation (Beletsky equation) of the second order with periodic coefficients and two parameters. The equation is equivalent to a periodic Hamiltonian system with a single degree of freedom and has a singularity. It turned out that two-parameter families of the generalized periodic solutions to this simple equation form complicated structures of a new type. A comparison of numerous separate results made it possible to outline a sufficiently unified and complete picture of the location and structure of the families of generalized 2-periodic solutions with an integer number of rotation. These families are compared with known data related to the resonance rotations of the natural satellites in the solar system.